The conversion of David Luiz from an error-prone central defender to a free-running midfielder capable of causing, and preying on, others’ errors may prove as valuable a part of Rafael Benitez’s achievement for Chelsea as the much-vaunted restoration of Fernando Torres’s powers as a striker.

It may also be a crucial factor in a change less to the taste of Chelsea’s fans, namely the ending of Frank Lampard’s days in their colours.

Torres, perhaps cowed by suggestions of David Villa’s possible arrival as competition for his place, was so ineffective at Norwich yesterday that one had to check the team sheet at half-time to confirm that he was indeed on it. His strike partner and fellow Spaniard Juan Mata, meanwhile, scored a splendid winning goal, while Luiz, doing much vital ball-winning in advanced areas, ran the show – though his shooting needs a lot of work before it comes near the Lampard class.

Interim manager Benitez is not ready to write off Lampard just yet, despite the midfielder seeming to be on his way in the January transfer window. “He’s under contract, he’s a good player; his future is a matter between him and the club. I will use him [and Ashley Cole, whose contract is also up in the summer] as I see fit as long as they are available,” Benitez said. “It’s important to have different players, different types of player, to give us different options.”

If one of those options proves to be a move to bring in Villa from Barcelona, then Benitez is not letting on. “We don’t talk about these things,” he said. “It’s important for any team to do these things in private.” Asked whether he was confident of improving the Chelsea team, he replied: “Yes. There are a lot of ways to improve a team [other than signing new players].”

Chelsea emerged to chants from their followers of “Super Frankie Lampard” – the 34-year-old, reduced to bench duty, did not appear in person until the 73rd minute – and it was not long before they were regaled with a lengthy chorus of “There’s only one Di Matteo” in reference to their former manager. Benitez has more to do yet to win the fans’ favour even after the eight-goal show against Aston Villa that preceded this more down-to-earth victory – one that seldom looked in doubt, though as Benitez said, “at 1-0 a quick counter-attack can always make a difference”.

The Spaniard added: “We were working hard. We have another clean sheet and we showed we could manage, we could control, against a good team. We’re in a good position but we can improve.”

Though the Londoners showed plenty of endeavour, mostly in the cause of closing down any Norwich player in possession or potential possession, it was 19 minutes before they produced a real shot, and that attempt from Luiz went closer to clearing the stadium roof than troubling Mark Bunn in the City goal. It was Luiz, however, given free rein by Benitez to venture forward at will – into Lampard’s place, you might say – who created the first clear chance in the 30th minute, robbing Wes Hoolahan to set up Mata, who found the side-netting from close range. But an increase in pressure by Benitez’s side was rewarded in the 38th minute with a finish of high class from Mata, whose shot from the edge of the penalty arc left Bunn flailing at fresh air as it lodged in the far corner of his net.

The strike impressed the Norwich City manager, Chris Hughton, who said: “That’s why clubs like Chelsea pay the amounts of money they do for offensive players. It was probably the one moment of real quality in the game.”

It was hard, after it, to see Norwich gaining anything from a game in which they had worked hard but been able to create little, and their loss might have been heavier but for Bunn, who made good second-half saves from Victor Moses – who also shot just wide after bringing down a cross superbly on his chest – and from Mata’s attempt to deceive him with a quickly-taken free-kick.

“If the team’s playing well, a clever player like Mata can make the difference,” Benitez said. Quite.